I experienced this. I never needed to lose weight, always been lean. But I wanted to see if I could reduce my blood sugar since it was borderline high. So I went very low carb for a while. Did not intend to but lost 5 kilos right away and felt fine, although it seemed like I was a bit underweight. A few weeks later got a miserable case of flu and couldn't eat for a few days. Lost even more weight, felt terrible, looked like death. It seems like the little reserves I previously had were gone from my change in diet.

Does it really need stored energy? Parenteral nutrition in hospital works fine with plain glucose. One would assume you could just eat fruit (or drink soda, I guess) when sick, to get the energy you need right then.